def test_threading(self):
np.random.seed(0)
m = 20
n = 10
As, bs, cs, cone_dicts = [], [], [], []
results = []
for _ in range(50):
A, b, c, cone_dims = utils.least_squares_eq_scs_data(m, n)
As += [A]
bs += [b]
cs += [c]
cone_dicts += [cone_dims]
results.append(cone_prog.solve_and_derivative(A, b, c, cone_dims))
for n_jobs in [1, -1]:
xs, ys, ss, _, DT_batch = cone_prog.solve_and_derivative_batch(
As, bs, cs, cone_dicts, n_jobs_forward=n_jobs, n_jobs_backward=n_jobs)
for i in range(50):
np.testing.assert_allclose(results[i][0], xs[i])
np.testing.assert_allclose(results[i][1], ys[i])
np.testing.assert_allclose(results[i][2], ss[i])
dAs, dbs, dcs = DT_batch(xs, ys, ss)
for i in range(50):
dA, db, dc = results[i][-1](results[i][0], results[i][1], results[i][2])
np.testing.assert_allclose(dA.todense(), dAs[i].todense())
np.testing.assert_allclose(dbs[i], db)
np.testing.assert_allclose(dcs[i], dc)
def test_threading(self):
m = 20
n = 10
As, bs, cs, cone_dicts = [], [], [], []
results = []
serial_time = 0.0
for _ in range(50):
A, b, c, cone_dims = utils.least_squares_eq_scs_data(m, n)
As += [A]
bs += [b]
cs += [c]
cone_dicts += [cone_dims]
tic = time.time()
results.append(cone_prog.solve_and_derivative(A, b, c, cone_dims))
toc = time.time()
serial_time += toc - tic
tic = time.time()
results_thread = cone_prog.solve_and_derivative_batch(
As, bs, cs, cone_dicts)
toc = time.time()
parallel_time = toc - tic
self.assertTrue(parallel_time < serial_time)
for i in range(50):
np.testing.assert_allclose(results[i][0], results_thread[i][0])
np.testing.assert_allclose(results[i][1], results_thread[i][1])
np.testing.assert_allclose(results[i][2], results_thread[i][2])
def test_ecos_solve(self):
np.random.seed(0)
m = 20
n = 10
A, b, c, cone_dims = utils.least_squares_eq_scs_data(m, n)
cone_dims.pop("q")
cone_dims.pop("s")
cone_dims.pop("ep")
x, y, s, derivative, adjoint_derivative = cone_prog.solve_and_derivative(
A, b, c, cone_dims, solve_method="ECOS")
# check optimality conditions
np.testing.assert_allclose(A @ x + s, b, atol=1e-8)
np.testing.assert_allclose(A.T @ y + c, 0, atol=1e-8)
np.testing.assert_allclose(s @ y, 0, atol=1e-8)
np.testing.assert_allclose(s,
cone_lib.pi(
s,
cone_lib.parse_cone_dict(cone_dims),
dual=False),
atol=1e-8)
np.testing.assert_allclose(y,
cone_lib.pi(
y,
cone_lib.parse_cone_dict(cone_dims),
dual=True),
atol=1e-8)
x = cp.Variable(10)
prob = cp.Problem(
cp.Minimize(
cp.sum_squares(np.random.randn(5, 10) @ x) +
np.random.randn(10) @ x), [
cp.norm2(x) <= 1,
np.random.randn(2, 10) @ x == np.random.randn(2)
])
A, b, c, cone_dims = utils.scs_data_from_cvxpy_problem(prob)
x, y, s, derivative, adjoint_derivative = cone_prog.solve_and_derivative(
A, b, c, cone_dims, solve_method="ECOS")
# check optimality conditions
np.testing.assert_allclose(A @ x + s, b, atol=1e-8)
np.testing.assert_allclose(A.T @ y + c, 0, atol=1e-8)
np.testing.assert_allclose(s @ y, 0, atol=1e-8)
np.testing.assert_allclose(s,
cone_lib.pi(
s,
cone_lib.parse_cone_dict(cone_dims),
dual=False),
atol=1e-8)
np.testing.assert_allclose(y,
cone_lib.pi(
y,
cone_lib.parse_cone_dict(cone_dims),
dual=True),
atol=1e-8)
def test_warm_start(self):
np.random.seed(0)
m = 20
n = 10
A, b, c, cone_dims = utils.least_squares_eq_scs_data(m, n)
x, y, s, _, _ = cone_prog.solve_and_derivative(
A, b, c, cone_dims, eps=1e-11)
x_p, y_p, s_p, _, _ = cone_prog.solve_and_derivative(
A, b, c, cone_dims, warm_start=(x, y, s), max_iters=1)
np.testing.assert_allclose(x, x_p, atol=1e-7)
np.testing.assert_allclose(y, y_p, atol=1e-7)
np.testing.assert_allclose(s, s_p, atol=1e-7)
def test_solve_and_derivative(self):
np.random.seed(0)
m = 20
n = 10
A, b, c, cone_dims = utils.least_squares_eq_scs_data(m, n)
for mode in ["lsqr", "dense"]:
x, y, s, derivative, adjoint_derivative = cone_prog.solve_and_derivative(
A, b, c, cone_dims, eps=1e-10, mode=mode, solve_method="SCS")
dA = utils.get_random_like(
A, lambda n: np.random.normal(0, 1e-6, size=n))
db = np.random.normal(0, 1e-6, size=b.size)
dc = np.random.normal(0, 1e-6, size=c.size)
dx, dy, ds = derivative(dA, db, dc)
x_pert, y_pert, s_pert, _, _ = cone_prog.solve_and_derivative(
A + dA,
b + db,
c + dc,
cone_dims,
eps=1e-10,
solve_method="SCS")
np.testing.assert_allclose(x_pert - x, dx, atol=1e-8)
np.testing.assert_allclose(y_pert - y, dy, atol=1e-8)
np.testing.assert_allclose(s_pert - s, ds, atol=1e-8)
x, y, s, derivative, adjoint_derivative = cone_prog.solve_and_derivative(
A, b, c, cone_dims, eps=1e-10, mode=mode, solve_method="SCS")
objective = c.T @ x
dA, db, dc = adjoint_derivative(c, np.zeros(y.size),
np.zeros(s.size))
x_pert, _, _, _, _ = cone_prog.solve_and_derivative(
A + 1e-6 * dA,
b + 1e-6 * db,
c + 1e-6 * dc,
cone_dims,
eps=1e-10,
solve_method="SCS")
objective_pert = c.T @ x_pert
np.testing.assert_allclose(objective_pert - objective,
1e-6 * dA.multiply(dA).sum() +
1e-6 * db @ db + 1e-6 * dc @ dc,
atol=1e-8)
def test_solve_and_derivative(self):
m = 20
n = 10
A, b, c, cone_dims = utils.least_squares_eq_scs_data(m, n)
x, y, s, derivative, _ = cone_prog.solve_and_derivative(A,
b,
c,
cone_dims,
eps=1e-8)
dA = utils.get_random_like(A,
lambda n: np.random.normal(0, 1e-6, size=n))
db = np.random.normal(0, 1e-6, size=b.size)
dc = np.random.normal(0, 1e-6, size=c.size)
dx, dy, ds = derivative(dA, db, dc)
x_pert, y_pert, s_pert, _, _ = cone_prog.solve_and_derivative(
A + dA, b + db, c + dc, cone_dims, eps=1e-8)
np.testing.assert_allclose(x_pert - x, dx, atol=1e-6, rtol=1e-6)
import cvxpy as cp
import numpy as np
from scipy import sparse
from scipy.sparse import linalg as splinalg
import time
import diffcp.cone_program as cone_prog
import diffcp.cones as cone_lib
import diffcp.utils as utils
m = 100
n = 50
A, b, c, cone_dims = utils.least_squares_eq_scs_data(m, n)
for mode in ["lsqr", "dense"]:
x, y, s, derivative, adjoint_derivative = cone_prog.solve_and_derivative(
A, b, c, cone_dims, eps=1e-10, mode=mode)
dA = utils.get_random_like(
A, lambda n: np.random.normal(0, 1e-2, size=n))
db = np.random.normal(0, 1e-2, size=b.size)
dc = np.random.normal(0, 1e-2, size=c.size)
derivative_time = 0.0
for _ in range(10):
tic = time.time()
dx, dy, ds = derivative(dA, db, dc)
toc = time.time()
derivative_time += (toc - tic) / 10